Intrinsic perimeter, compactness and Poincaré inequality for SBV functions in Carnot-Carathéodory spaces

2025/10/22 by Marco Di Marco, Di Marco, Marco
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2510.19380

Abstract

By introducing an intrinsic perimeter measure for intrinsic countably rectifiable sets, we prove a compactness result and a Poincaré inequality for special functions with bounded variation in equiregular Carnot-Carathéodory spaces which satisfy an additional natural assumption, called property \mathcal R.

Citations

• SBV functions in Carnot-Carathéodory spaces
• Fine properties of functions with bounded variation in Carnot-Carathéodory spaces
• The Gauss-Green theorem in stratified groups
• A compactness result for BV functions in metric spaces
• Rank-one theorem and subgraphs of BV functions in Carnot groups
• BV functions and sets of finite perimeter in sub-Riemannian manifolds
• Regularity of sets with constant intrinsic normal in a class of Carnot\n groups
• Two characterization of BV functions on Carnot groups via the heat semigroup
• An extension and trace theorem for functions of H-bounded variation in Carnot groups of step 2

Related

• SBV functions in Carnot-Carathéodory spaces
• A compactness result for BV functions in metric spaces
• Tangency sets of non-involutive distributions and unrectifiability in Carnot-Carathéodory spaces
• BV Functions and Sets of Finite Perimeter on Configuration Spaces
• Two characterization of BV functions on Carnot groups via the heat semigroup